## Frequency Distributions Exercise

1. For the following scores, find:

(a) The median
(b) The mode
(c) The mean

(i) 8, 6, 4, 9, 3, 3, 2

(ii) 101, 99, 100, 98, 101, 104, 96, 101

(iii) 10, 12, 12, 12, 20

(iv) 50, 30, 20, 20, 10, 5

2. A golfer plays seven rounds of golf in a week. His scores are: 70, 62, 62, 69, 71, 72, 80

 (a) Calculate the mean, median and mode of these seven scores. (b) Which of these averages would not be very representative of his week's golf. 3. A girl had a newspaper delivery round. Her weekly pay for 2 month's work was:

\$12.50, \$11.80, \$10.70, \$13.10, \$4.50, \$12.00, \$9.20, \$9.60

(a) What was her mean weekly pay?

(b) What was her median pay?

(c) What was the difference between her highest and lowest pays?

4. The diagram shows the height of plants, measured in centimetres. (a) How many plants were measured?

(b) What was the median plant height?

(c) What percentage of plants were over 45 cm high?

(d) What percentage of plants were less than 30 cm high?

(e) How many plants were between 50 and 60 cm high?

5. The following set of marks were for a class of 20 pupils. The test was out of 10 marks.

5, 6, 6, 3, 2, 5, 7, 6, 4, 7, 2, 0, 1, 4, 5, 6, 6, 7, 3, 8

(a) Construct a frequency distribution table.
(b) Draw a frequency histogram.
(c) Draw a frequency curve.
(d) Calculate the mean mark.
(e) Find the median mark.
(f) What is the mode?
(g) What is the probability that a person picked at random would score

(i) Seven? (ii) Less than 5?

6. The frequency distribution for the length, in seconds, of 100 telephone calls was:

 Time (seconds) Frequency 0 − 20 0 21 − 40 5 41 − 60 7 61 − 80 14 81 − 100 28 101 − 120 21 121 − 140 13 141 − 160 9 161 − 180 3

(a) Construct a cumulative frequency table.

(b) Draw a cumulative frequency graph.

(c) What number of calls lasted no more than 2 minutes?

(d) What is the probability that a call picked at random lasted more than 140 seconds?

(e) What percentage of calls lasted more than 1 minute?

7. State whether the following would be discrete or continuous data:

(a) The weights of people.

(b) The number of people at a concert.

(c) The heights of trees.

(d) A person's shoe size.

8. The following list is the temperatures, in °C, at 20 main centres of New Zealand for a day in January.

23, 27, 19, 28, 24, 26, 27, 24, 18, 23, 15, 24, 23, 22, 24, 29, 16, 24, 22, 25

(a) Construct a frequency table with class intervals of 3°C.

(b) Draw a histogram to illustrate this distribution.

(c) What is the modal temperature range?

(d) Calculate the mean temperature.

(e) What would the median temperature be?

(f) What is the probability that a centre picked at random would have a temperature greater than or equal to 21°C?

9. The cumulative frequency graph shows the volume of drink in cans of soft drink.

 (a) How many cans of soft drink were measured? (b) How many cans contained: (i) Less than 350 mL?(ii) More than 340 mL?(iii) Between 320 and 370 mL? (c) What is the probability that a randomly selected can of drinkwill contain less than 350 mL? (d) If 4000 cans were produced, how many would you expect to contain less than 350 mL? (e) What is the median amount of drink in a can? 10. The table shows the lengths of 17 New Zealand rivers.

Show this information on an ordered stem and leaf diagram, using the first two digits as the stem.

 Name of river Length (in km) Waiau 169 Waiau (Southland) 217 Waimakariri 161 Clarence 209 Waitaki 209 Rangitaiki 193 Manawatu 182 Waihou 175 Mohaka 172 Oreti 203 Wairau 169 Rakaia 145 Whangehu 161 Patea 143 Mokau 158 Ngarurora 154 Buller 177

11. The final examination results of two classes are to be compared.

The results are shown below:

 First class 53 43 67 87 36 56 76 45 87 73 45 53 74 65 38 71 40 33 59 Second class 46 45 47 67 56 59 66 50 79 80 35 55 77 55 30 65 42 39 39

(a) Draw a stem and leaf diagram for each class.

(b) Arrange each set of results in order and calculate the median and the upper and lower quartiles.

(c) Draw box and whisker plots, side by side and compare the results of the two classes.